Question

What would be a situation in which the length of a right triangle are known but the measure of an angle is needed?

Answer 1

If the length of at least 2 sides are known, the length of all sides and the measure of all of it's angles can be found out by using trigonometry.

Explanation:

For this, we need the length of at least two sides of the right angled triangle.If the triangle is triangle ABC and one of the sides (let BC) be the hypotenuse, then,

by Pythagoras theorem we get,

`(AB)^(2) + (AC)^(2) = (BC)^(2)` -------(1)

So, from (1), given the length of two sides of the triangle, we will be able to find the length of the other side of the triangle.

Now,

if one of the angles say ∠ABC be equal to θ then it can be calculated from the relation,

θ =
`\tan^(-1)((AC)/(AB))` -----(2)

and one of the other angles, say β = ∠ACB can be obtained from the relation

θ + β = 90° -----------(3)

and we know ∠BAC = 90° ---------(4)

So, all the angles are thus obtained.